Today, no french common name looks like Sarcher. Only "chercher" is a little phoneticaly similar. On the other hand, if we search in an old french dictonary we can find some words that could be used to construct the name :
(I only translate a summary of what we found, if you want more details, refer to the french page about the subject.)
Une sarche : A wood circle used to make a sieve, it is also a thin double-breasted material.
Un sarchet : (also sarchel) weeding hoe.
Un sarchel : Spur to prick oxen.
Une sarchele : species of wood to make hoops.
Un Sarchier, sarchière : It is the curate of the most senior member of a chapter. A sarchière is also someone who mends.
Sarcher : To make efforts to find someone or something.